To determine the minimum amount Rafael should charge per cup of punch, we first need to calculate the overall cost of the ingredients, then add the desired profit, and finally divide by the number of cups.
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Costs of the Ingredients:
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Sorbet: Rafael needs 1 gallon of raspberry sorbet. Since there are 4 quarts in a gallon and he pays $4.00 per quart, the cost of the sorbet is: \[ 4 \text{ quarts} \times $4.00/\text{quart} = $16.00 \]
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Lemon-lime soda: Rafael needs 2 liters of soda. He pays $3.00 for a 2-liter container, so the cost of the soda is: \[ $3.00 \]
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Total Cost: \[ \text{Total cost} = \text{Cost of sorbet} + \text{Cost of soda} = $16.00 + $3.00 = $19.00 \]
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Desired Profit: Rafael wants to make a profit of $10: \[ \text{Total revenue needed} = \text{Total cost} + \text{Profit} = $19.00 + $10.00 = $29.00 \]
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Price per Cup: Since Rafael makes 12 cups, the price per cup should be: \[ \text{Price per cup} = \frac{\text{Total revenue needed}}{\text{Number of cups}} = \frac{29.00}{12} \]
Calculating this gives: \[ \text{Price per cup} = \frac{29.00}{12} \approx 2.4167 \]
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Rounding to the Nearest Hundredth: Rounding this to the nearest hundredth: \[ \text{Price per cup} \approx 2.42 \]
Thus, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.42.